Gain-phase relationships evaluation by Gaussian quadrature

Hilbert transform has been recognized as a very important method in circuit theory, communications and control science. Its sampled derivations have been encountered in different applications from science and engineering. In this paper, the gain-phase relationships are evaluated using Gaussian quadrature. First we recall the Hilbert transform and a part of the theoretical background of the Gaussian quadrature approach. The approximation of the Hilbert transform with Gaussian quadrature is described and examples of gain-phase relationships are presented. Finally we discuss the advantages and drawbacks of this Gaussian approach.